Abstract Single-cell multi-omic datasets, in which multiple molecular modalities are profiled within the same cell, provide a unique opportunity to discover the temporal relationship between epigenome and transcriptome. To realize this potential, we propose to develop a system consisting of differential equations that extends the RNA velocity framework for gene expression to incorporate epigenomic data. By fitting pairs of jointly sequenced RNA-seq and ATAC-seq data, this probabilistic latent variable model is able to estimate the switch time and rate parameters of chromatin accessibility and gene expression from single-cell data, providing a quantitative summary of the temporal relationship between epigenomic and transcriptomic changes. The parameters inferred by the method quantify the length of time for which genes occupy each of the four distinct and biological meaningful states, ranking genes by the degree of coupling between transcriptome and epigenome. Similar to how transcriptomic data has been split into unspliced and spliced modalities to compute RNA velocity, the chromatin accessibility data measured with ATAC-seq can be further split into enhancers and promoters to model dynamics inside cis-regulatory networks during transcription. We will use this comprehensive multi-layer velocity method to study human blood cell differentiation and mechanistic changes during transcription due to HIV infection. We seek to uncover previously unknown markers of infection status through the means of mathematical modeling on single-cell multi-omic sequencing techniques.